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A method for calculating intermolecular induction and dispersion energies based on aGW description of the monomers and employing response functions from the Bethe-Salpeter equation is proposed. Calculations on a test set of 10 weakly bound complexes with GW-based symmetry-adapted perturbation theory (GW-SAPT) show an improved performance in comparison with symmetry-adapted perturbation theory based on density-functional theory (DFT-SAPT). [ABSTRACT FROM AUTHOR]

An automated implementation of the incremental scheme for the computation of MP2-F12 and CCSD(F12) energies is presented. The numerical accuracy of the approach is explored for a set of 15 chemical reactions using the limiting case of single orbital one-site domains as a worst case scenario. The results are analyzed by the maximum absolute deviation, the mean absolute error, and the root mean square error, with respect to the standard MP2-F12 and CCSD(F12) results. It is found that the MP2 reaction energies are within 1 kcal/mol accuracy at third order of the expansion, whereas the F12 corrections are already sufficiently accurate at second order. For the CCSD(F12) method 1 kcal/mol accuracy is obtained at fourth order. [ABSTRACT FROM AUTHOR]

Second-order perturbation theory using explicitly correlated wave functions has been introduced into a quasirelativistic two-component formalism. The convergence of the correlation energy is as much improved as for the nonrelativistic Hamiltonian, achieving basis-set-limit results in a moderate-size basis set. Equilibrium distances and vibrational frequencies of small molecules of the 6th period of the periodic system of the elements have been calculated, demonstrating the improved behavior of the explicitly correlated wave functions. Taking advantage of density-fitting techniques, the explicitly correlated approach is an economical and appealing alternative to conventional two-component second-order perturbation theory in a large one-particle basis. [ABSTRACT FROM AUTHOR]

The photoelectron spectrum (PES) of the uracil anion is reported and discussed from the perspective of quantum chemical calculations of the vertical detachment energies (VDEs) of the anions of various tautomers of uracil. The PES peak maximum is found at an electron binding energy of 2.4 eV, and the width of the main feature suggests that the parent anions are in a valence rather than a dipole-bound state. The canonical tautomer as well as four tautomers that result from proton transfer from an NH group to a C atom were investigated computationally. At the Hartree–Fock and second-order Mo\ller-Plesset perturbation theory levels, the adiabatic electron affinity (AEA) and the VDE have been converged to the limit of a complete basis set to within ±1 meV. Post-MP2 electron-correlation effects have been determined at the coupled-cluster level of theory including single, double, and noniterative triple excitations. The quantum chemical calculations suggest that the most stable valence anion of uracil is the anion of a tautomer that results from a proton transfer from N1H to C5. It is characterized by an AEA of 135 meV and a VDE of 1.38 eV. The peak maximum is as much as 1 eV larger, however, and the photoelectron intensity is only very weak at 1.38 eV. The PES does not lend support either to the valence anion of the canonical tautomer, which is the second most stable anion, and whose VDE is computed at about 0.60 eV. Agreement between the peak maximum and the computed VDE is only found for the third most stable tautomer, which shows an AEA of ≈-0.1 eV and a VDE of 2.58 eV. This tautomer results from a proton transfer from N3H to C5. The results illustrate that the characteristics of biomolecular anions are highly dependent on their tautomeric form. If indeed the third most stable anion is observed in the experiment, then it remains an open question why and how this species is formed under the given conditions. [ABSTRACT FROM AUTHOR]

A valence-type anion of the canonical tautomer of uracil has been characterized using explicitly correlated second-order Mo\ller-Plesset perturbation theory (RI-MP2-R12) in conjunction with conventional coupled-cluster theory with single, double, and perturbative triple excitations. At this level of electron-correlation treatment and after inclusion of a zero-point vibrational energy correction, determined in the harmonic approximation at the RI-MP2 level of theory, the valence anion is adiabatically stable with respect to the neutral molecule by 40 meV. The anion is characterized by a vertical detachment energy of 0.60 eV. To obtain accurate estimates of the vertical and adiabatic electron binding energies, a scheme was applied in which electronic energy contributions from various levels of theory were added, each of them extrapolated to the corresponding basis-set limit. The MP2 basis-set limits were also evaluated using an explicitly correlated approach, and the results of these calculations are in agreement with the extrapolated values. A remarkable feature of the valence anionic state is that the adiabatic electron binding energy is positive but smaller than the adiabatic electron binding energy of the dipole-bound state. [ABSTRACT FROM AUTHOR]

The analytic calculation of first-order properties has been implemented in the DALTON program at the level of explicitly correlated second-order Mo\ller-Plesset perturbation theory (MP2-R12). The implementation has been accomplished for MP2-R12 theory based on standard approximations A, A′, and B, using an auxiliary basis for the resolution-of-the-identity approximation, with and without a frozen core. MP2-R12 first-order molecular properties have been calculated analytically for a few small test molecules. For BH and HF, the MP2-R12 results were supplemented with explicitly correlated coupled-cluster calculations (but at this level from numerical derivatives) including vibrational and relativistic corrections. [ABSTRACT FROM AUTHOR]

A simplified singles-and-doubles linear-r12 corrected coupled-cluster model, denoted CCSD(R12), is proposed and compared with the complete singles-and-doubles linear-r12 coupled-cluster method CCSD-R12. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation to calculate three-electron integrals needed in the linear-r12 Ansatz. Basis-set convergence is investigated for a selected set of atoms and small molecules. In a large basis, the CCSD(R12) model provides an excellent approximation to the full linear-r12 energy contribution, whereas the magnitude of this contribution is significantly overestimated at the level of second-order perturbation theory. [ABSTRACT FROM AUTHOR]

In the framework of second-order Møller—Plesset linear-r12 MP2-R12 perturbation theory, a method is developed and implemented that uses an auxiliary basis set for the resolution-of-the-identity RI approximation for the three- and four-electron integrals. In contrast to previous work, the two-electron integrals that must be evaluated never involve more than one auxiliary basis function. The new method therefore scales linearly with the number of auxiliary basis functions and is much more efficient than the previous one, which scaled quadratically. A general formulation of MP2-R12 theory is presented for various ansätze, approximations, and orbitals (canonical or localized). The new method is assessed by computations of the valence-shell second-order Møller—Plesset correlation energy of a few small closed-shell systems. The preliminary calculations indicate that the difference between the new and previous methods is about one order of magnitude smaller than the errors that occur due to basis-set truncations and RI approximations and under the assumptions of generalized and extended Brillouin conditions. [ABSTRACT FROM AUTHOR]

Starting from the Le´vy-Leblond equation, which is the four-component nonrelativistic limit of the Dirac equation, a direct perturbation theory of magnetic properties and relativistic corrections is developed and implemented for point-charge and finite nuclei. The perturbed small components are regularized by projecting them onto an auxiliary small-component basis of Gaussian functions. The relevant operators and matrix elements are derived for the point-nuclear and Gaussian nuclear models. It is demonstrated how the usual paramagnetic spin-orbit, Fermi-contact, and spin-dipole integrals of Ramsey’s theory can be evaluated in the same manner as field and field-gradient integrals—that is, as derivatives of potential-energy integrals. A few illustrative calculations are performed. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A torsional potential energy surface for the cyclic water trimer was calculated at the level of second-order Mo\ller–Plesset perturbation theory. For the construction of this ab initio surface, the first-order wave function was expanded in a many-electron basis which linearly depends on the interelectronic coordinates r12. The one-electron basis of Gaussian orbitals was calibrated on the water monomer and dimer to ensure that the ab initio surface computed represents the (near- ) basis set limit for the level of theory applied. The positions of the free O—H bonds are described by three torsional angles. The respective three-dimensional torsional space was investigated by 70 counterpoise corrected single-point calculations for various values of these angles, providing a grid to fit an analytical representation of the potential energy surface. The four symmetry unique stationary points previously found at the Hartree–Fock and conventional Mo\ller–Plesset levels [Schütz et al., J. Chem. Phys. 99, 5228 (1993)] were studied in detail: Relative energies of the structures were calculated by applying second-order Mo\ller–Plesset and coupled cluster methods; harmonic vibrational frequencies were calculated at the second-order Mo\ller–Plesset level with a 6-311++G(d,p) basis set at these stationary points. It is expected that the present torsional potential energy surface for the water trimer will play an important role in the understanding of the vibrational transitions observed by far-infrared vibration–rotation–tunneling spectroscopy in terms of a nearly free pseudorotational interconversion on a cyclic vibrational–tunneling path. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The matrix elements needed in a CI-SD, CEPA, MP2, or MP3 calculation with linear r12-dependent terms for closed-shell states are derived, both exactly and in a consistent approximate way. The standard approximation B guarantees that in the atomic case the error due to truncation of the basis at some angular momentum quantum number L goes as ∼L-7, at variance with L-3 in conventional calculations (without r12 terms). Another standard approximation A has errors ∼L-5, but is simpler and—for moderate basis sets—somewhat better balanced. The explicit expressions for Mo\ller–Plesset perturbation theory of second and third order with linear r12 terms (MP2-R12 and MP3-R12, respectively) are explicitly given in the two standard approximations. [ABSTRACT FROM AUTHOR]

The MP2-R12 method (Mo\ller–Plesset second-order perturbation theory with terms linear in the interelectronic coordinate r12) in the approximations A and B as outlined in paper I of this series is applied to the ground states of the molecules H2, LiH, HF, H2O, NH3, CH4, Be2, N2, F2, C2H2, and CuH in their experimental equilibrium geometry, and to the van der Waals interaction between two He atoms. In all cases MP2 correlation energies are obtained that are supposed to differ by at most a few percent from the basis set limit. For CH4 the dependence of the energy on the symmetric stretching coordinate is studied, which together with other information leads to a recommended bond length of 1.086 Å for the CH bond length. For He2 and F2 the canonical and localized descriptions are compared. The latter is superior for the K-shell contributions, otherwise there is a little difference. For He2 in the localized representation rather good results for the dispersion interaction are obtained. The potential curve of Be2 is significantly improved in MP2-R12 as compared to conventional MP2. The examples C2H2 and CuH show that the method is not limited to very small systems. [ABSTRACT FROM AUTHOR]

Interference-corrected explicitly correlated second-order perturbation theory (INT-MP2-F12) is applied to accelerate the convergence to the complete-basis-set limit of coupled-cluster computations. Adding energy terms obtained from INT-MP2-F12 theory to the energies obtained from coupled-cluster singles-and-doubles (CCSD) computations yields a mean absolute deviation (MAD) from explicitly correlated CCSD results below 1 kJ/mol for a test set of 106 molecules. A composite scheme for the computation of atomization energies is assessed. This scheme is denoted as CCSD(T)+F12+INT and consists of the CCSD model with perturbative triples (CCSD(T)) supplemented with INT-MP2-F12 corrections, using a quadruple-zeta quality basis set (cc-pVQZ-F12). The composite scheme achieves chemical accuracy with respect to experimentally derived or computed reference values. Using Boys localized molecular orbitals, the MAD of the CCSD(T)+F12+INT/cc-pVQZ-F12 atomization energies from the reference values is below 1 kJ/mol for the G2/97 test set. [ABSTRACT FROM AUTHOR]

Non-covalent interactions can usually be described accurately at the coupled-cluster level of theory using single, double and triple excitations, the latter within a perturbation-theory framework. However, since the computations with the corresponding coupled-cluster model, CCSD(T), are computationally very demanding, they can often not be carried out in large enough basis sets. This leads to a basis-set truncation error. To correct this error, a basis-set correction can be computed at the level of second-order Møller–Plesset (MP2) perturbation theory in the limit of a complete basis set, but such a correction tends to overestimate the magnitude of the basis-set truncation error. In the present work, we suggest to damp the basis-set correction obtained at the complete-basis-set MP2 level using interference factors for individual occupied orbital pairs. The approach is applied to the non-covalent interactions of the S22B database, where the interference correction turns out to be very small. [ABSTRACT FROM AUTHOR]

A detailed description of the explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12) method, as implemented in the T program package, is presented. The T implementation makes use of density fitting, which greatly reduces the prefactor for integral evaluation. Methods are available for the treatment of ground states of open- and closed-shell species, using unrestricted as well as restricted (open-shell) Hartree-Fock reference determinants. Various methodological choices and approximations are discussed. The performance of the T implementation is illustrated by example calculations of the molecules leflunomide, prednisone, methotrexate, ethylenedioxytetrafulvalene, and a cluster model for the adsorption of methanol on the zeolite H-ZSM-5. Various basis sets are used, including the correlation-consistent basis sets specially optimized for explicitly correlated calculations (cc-pVXZ-F12). © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011 [ABSTRACT FROM AUTHOR]

Abstract: The atomization energies of the 105 molecules in the test set of Bakowies [D. Bakowies, J. Chem. Phys. 127 (2007) 084105] have been computed with an estimated standard deviation (from the values compiled in the Active Thermochemical Tables) of ±0.1kJ/mol per valence electron in the molecule. Equilibrium geometries and harmonic vibrational frequencies were calculated at the all-electron CCSD(T)/cc-pCVTZ level, that is, at the level of coupled-cluster theory with singles, doubles and non-iterative triples in a correlation-consistent polarized core–valence triple-zeta basis. Single-point energy calculations were performed at the all-electron CCSD(T) level in a correlation-consistent polarized core–valence quadruple-zeta basis (cc-pCVQZ), and several corrections were added: (i) a correction for the basis-set truncation error, obtained from second-order perturbation theory using Slater-type geminals (MP2-F12 theory), (ii) a correction for the effect of anharmonicity on the zero-point vibrational energy, (iii) a relativistic correction, (iv) a correction for the difference between the full CCSDT model (coupled-cluster theory with singles, doubles and triples) and the CCSD(T) approximation, and (v) a correction for connected quadruple excitations obtained from CCSDT(Q) calculations. The correction for the basis-set truncation error was obtained from MP2-F12 calculations by scaling the MP2 basis-set truncation error by an empirically optimized “interference factor” of f int =0.78. The reference values from the Active Thermochemical Tables for 73 molecules in the test set, the equilibrium geometries, the harmonic vibrational frequencies, and all of the energy corrections represent valuable data for performance assessments of additivity schemes that will be developed in the future, in which the basis-set truncation error will be calculated at the level of coupled-cluster theory using Slater-type geminals (CC-F12 theory). Such a scheme will be free of empirical corrections and scaling factors. [Copyright &y& Elsevier]

Slater-type geminals (STGs) have been used as explicitly correlated two-electron basis functions for calculations on the hydrides of N–As and Sb (as well as on the hydrides of O–Se and F–Br with similar, not reported results) in various one-electron basis sets of Gaussian atomic orbitals. The performance of the explicitly correlated theory has been assessed with respect to the exponent of the STG, for example, by using different exponents for individual pair correlation functions and pair energies. It is shown that a correlation factor with an exponent of $${\gamma = 1.4 a_{0}^{-1}}$$ can give reliable results within 1% from the basis-set limit for all investigated molecules in an aug-cc-pVQZ basis set for the valence shells, using fixed amplitudes for the STGs in a diagonal orbital-invariant formulation of the theory. The use of relativistic effective core potentials (RECPs) in explicitly correlated second-order perturbation theory has been investigated. [ABSTRACT FROM AUTHOR]

The introduction of the resolution-of-the-identity (RI) approximation for electron repulsion integrals in quantum chemical calculations requires in addition to the orbital basis so-called auxiliary or fitting basis sets. We report here such auxiliary basis sets optimized for second-order Møller–Plesset perturbation theory for the recently published (Weigend and Ahlrichs Phys Chem Chem Phys, 2005, 7, 3297–3305) segmented contracted Gaussian basis sets of split, triple-ζ and quadruple-ζ valence quality for the atoms Rb–Rn (except lanthanides). These basis sets are designed for use in connection with small-core effective core potentials including scalar relativistic corrections. Hereby accurate resolution-of-the-identity calculations with second-order Møller–Plesset perturbation theory (MP2) and related methods can now be performed for molecules containing elements from H to Rn. The error of the RI approximation has been evaluated for a test set of 385 small and medium sized molecules, which represent the common oxidation states of each element, and is compared with the one-electron basis set error, estimated based on highly accurate explicitly correlated MP2–R12 calculations. With the reported auxiliary basis sets the RI error for MP2 correlation energies is typically two orders of magnitude smaller than the one-electron basis set error, independent on the position of the atoms in the periodic table. [ABSTRACT FROM AUTHOR]

We present the extension of a recently proposed universal explicit electron correlation (F12) correction for multi-reference perturbation theories to general complete active spaces and arbitrary choices of complete active space self-consistent field (CASSCF) orbitals. This F12 correction is applied to Mukherjee's multi-reference second-order perturbation theory (Mk-MRPT2). Pilot examples show the expected reduction of the basis sets incompleteness error of about two cardinal numbers. [ABSTRACT FROM AUTHOR]

A recently proposed computational protocol is employed to obtain highly accurate atomization energies for the full G2/97 test set, which consists of 148 diverse molecules. This computational protocol is based on the explicitly correlated coupled-cluster method with iterative single and double excitations as well as perturbative triple excitations, using quadruple-ζ basis sets. Corrections for higher excitations and core/core-valence correlation effects are accounted for in separate calculations. In this manner, suitable reference values are obtained with a mean deviation of -0.75 kJ/mol and a standard deviation of 1.06 kJ/mol with respect to the active thermochemical tables. Often, in the literature, new approximate methods (e.g., in the area of density functional theory) are compared to, or fitted to, experimental heats of formation of the G2/97 test set. We propose to use our atomization energies for this purpose because they are more accurate on average. [ABSTRACT FROM AUTHOR]

Abstract: This article is concerned with the calculation of the two-electron Darwin term (D2). At the level of explicitly correlated second-order perturbation theory (MP2-F12), the D2 term is obtained as an analytic energy derivative; at the level of explicitly correlated coupled-cluster theory, it is obtained from finite differences. To avoid the calculation of four-center integrals, a density-fitting approximation is applied to the D2 two-electron integrals without loss of accuracy, even though the absolute value of the D2 term is typically about 0.1mE h. Explicitly correlated methods provide a qualitatively correct description of the short-range region around the Coulomb hole, even for small orbital basis sets. Therefore, explicitly correlated wave functions remedy the otherwise extremely slow convergence of the D2 contribution with respect to the basis-set size, yielding more accurate results than those obtained by two-point basis-set extrapolation. Moreover, we show that the interference correction of Petersson’s complete-basis-set model chemistry can be used to compute a D2 basis-set correction at the MP2-F12 level to improve standard coupled-cluster singles-and-doubles results. [Copyright &y& Elsevier]